Perfect Set

In mathematics, in the field of topology, a perfect set is a closed set with no isolated points, and a perfect space is any topological space with no isolated points. In such spaces, every point can be approximated arbitrarily well by other points – given any point and any topological neighborhood of the point, there is another point within the neighborhood.The term perfect space is also used, incompatibly, to refer to other properties of a topological space, such as being a Gδ space. Context is required to determine which meaning is intended.In this article, a space which is not perfect will be referred to as imperfect.
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